|This is not entirely true. The outlet temperature of the turbo is a function of 3 things; the compressor efficiency, the pressure ratio and the inlet temperature. What you will find is that a 10* increase in inlet temperature will propagate into an outlet temperature that is more than 10* higher. When you get to higher pressure ratios and less efficient compressors, a small change in inlet temperature can lead to a significant change in outlet temperature.
edit - and once you get downstream to the intercooler, the hotter inlet temperature will allow more heat to be removed (in terms of Watts), but the outlet temperature of the intercooler will still be higher than it would have with a cooler compressor inlet temperature. As the effectiveness of the intercooler approaches 100%, the outlet temperature will all approach the same temperature (ambient!).